Download GEOMETRY EOC ASSESSMENT GUIDE

GEOMETRY EOC ASSESSMENT GUIDE
The Geometry End-of-Course (EOC) test assesses the Louisiana Student Standards for Mathematics (LSSM), which were revised by committees of Louisiana
educators during the 2015-2016 school year and approved by the State Board of Elementary and Secondary Education (BESE) in June 2016. The structure of the
test remains the same as it was in previous administrations. The Department has reviewed the existing question banks for Geometry to remove questions that
no longer align to the LSSM and to identify areas where test questions are needed due to new or revised standards. Similar to previous years’ tests, new
questions will be developed and embedded for new standards; for example, the statistics standards that are new to Geometry. This process allows districts time
to teach the new material and not hold students accountable for the new content in the 2016-2017 school year.
The purpose of this assessment guide is to assist educators in understanding:
• the structure of the test
• specifications for the multiple-choice and constructed-response sessions
• the standards eligible for assessment
• links to sample items and other resources
Louisiana Student Standards for Mathematics
The LSSM define what students should know and be able to do by the end of the Geometry course. The Geometry course is comprised of standards from the
following conceptual categories: Geometry and Statistics and Probability. Each operational test item is aligned to one or part of one standard from the Geometry
conceptual category of the LSSM. Test items aligned to statistics standards may appear as embedded field-test items.
Test Structure
The following table outlines the test structure and suggested testing times for the Geometry EOC test.
Test Session
Session 1: Multiple Choice, No Calculator
Session 2: Constructed-Response, Calculator
Session 3: Multiple Choice, Calculator
Totals
Number of Items 1
25
2
25
52
Number of Points
23
4
23
50
Suggested Testing Times
60 minutes
40 minutes
60 minutes
160 minutes
The test is untimed. Although suggested testing times are provided for each session, it is very important that students be given sufficient time to complete the
test. Once students have started a test session, they should proceed without interruption until they have completed the session.
1
Forty-six multiple-choice and one constructed-response items are operational. The other five items are embedded field test items, which may be used to develop new forms.
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Test Specifications
Test content is prioritized based on whether a standard is considered to be major, supporting, or additional content 2 for the work of Geometry. Major content
accounts for approximately 75% of tested material, while supporting and additional content account for approximately 25%. Supporting and additional content
should be incorporated throughout instruction of the major content. Neglecting any material will leave gaps in student knowledge and cause instructional
challenges in future courses. Constructed-response items may cover any content—major, supporting, or additional.
• Major content (green ) requires greater emphasis based on the depth of the ideas, mastery time, and/or importance to future mathematics or
demands of college and career readiness.
• Supporting content (blue ) supports and strengthens areas of major emphasis.
• Additional content (yellow ) bridges content from one course to the next, but may not establish tight or explicit connectivity to the major work of a
course.
Reporting Category
1
2
3
4
Conceptual Category – Domain
Geometry – Congruence
Geometry – Similarity, Right Triangles, and Trigonometry
Geometry – Circles
Geometry – Expressing Geometric Properties with Equations
Geometry – Geometric Measurement and Dimension
Geometry – Modeling with Geometry
Total
Total Points
10
20
Percentage of Points
20
40
10
20
10
20
50
100
Online Testing Platform
The 2016-2017 EOC tests will be administered on the same online system that was used to deliver the Spring 2016 computer-based tests for grades 3 through 8
in English language arts and mathematics and the social studies computer-based field tests. Students will enter their answers into the online testing system by
clicking on the circle next to the correct answer for multiple-choice questions. When composing their typed responses to the constructed-response questions,
students will type their responses into the boxes using the keyboard and equation builder.
Testing Materials
All students should receive scratch paper (lined, graph, and/or unlined) and two pencils from their test administrator.
Tool
scratch paper, graph paper, two pencils
inch ruler, centimeter ruler, and protractor
calculator
Geometry Reference Sheet
2
Provided
by Test Administrator
online
online and/or by Test Administrator
online and/or by Test Administrator
Session 1
YES
YES
NO
YES
Session 2
YES
YES
YES
YES
Session 3
YES
YES
YES
YES
For more information on content emphasis, consult the Geometry Remediation Guide.
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The online testing platform includes the following tools, which allow a student to select answer choices, “mark” items, eliminate answer options, use a calculator
for certain items, take notes, enlarge the item, guide the reading of a source or an item line by line, access the Geometry Reference Sheet, measure figures, and
use an equation builder for entering special characters. A help tool is also featured to assist students as they use the online system. Because this testing platform
provides students with an equation builder tool with open-response boxes, a Typing Help sheet is no longer necessary and will not be provided to students.
Teachers and students should practice using the equation builder tool and access the Guide to the EOC Equation Builder to prepare for this new platform
feature.
• Pointer tool
• Sticky Note tool
• Highlighter tool
• Magnifying tool
• Cross-Off tool
• Line Guide
• Calculator
• Geometry
Reference Sheet
• Measurement tools: protractor,
1
– inch ruler, centimeter ruler
8
• Equation Builder
• Help tool
All students should work through the Online Tools Training to practice using the online tools so they are well prepared to navigate the online testing system.
Rulers and protractor provided on the Geometry EOC test (not actual size):
To ensure accurate measurement, the size of the rulers, along with the object being measured, varies depending on the computer monitor’s resolution. Visit the
Online Tools Training (OTT) to practice using the online rulers and protractor. The ruler and protractor may not be available for some questions. If a tool is not
available, it will not appear when choosing the Measurement tools icon.
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Reference Sheet
Students taking the Geometry EOC test will have access to the Geometry Reference Sheet via the online testing platform and may also be provided an
unmarked/clean hardcopy from the test administrator.
Geometry EOC Reference Sheet
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Calculator Policy
The Geometry EOC test allows a scientific (with or without graphing capabilities) calculator during Sessions 2 and 3. Calculators are not allowed during Session 1
of the test. For students with the approved accommodation, a scientific calculator (with or without graphing capabilities) is allowed during all test sessions. The
student should use the calculator they have regularly used throughout the school year in their classroom and are most familiar with, provided their regular-use
calculator is not outside the boundaries of what is allowed. The following table includes calculator information by session for both general testers and testers
with approved accommodations for calculator use.
Calculator Policy
Session 1
Session 2
Session 3
Testers
Not allowed
Scientific (without graphing capabilities) available online, may
also have hand-held scientific (with or without graphing
Testers with approved
Must be provided hand-held scientific
capabilities)
accommodation for calculator use
(with or without graphing capabilities)
Additional information for testers with approved accommodations for calculator use:
• If a student needs an adaptive calculator (e.g., large key, talking), the student may bring his or her own or the school may provide one,
as long as it is specified in his or her approved IEP or 504 Plan.
Additionally, schools must adhere to the following guidance regarding calculators.
•
•
•
•
Calculators not permitted:
o Calculators with Computer Algebra System (CAS) features,
o Calculators with “QWERTY” keyboards,
o Calculators with paper tape
o Calculators that talk or make noise, unless specified in IEP/IAP
o Calculators on tablet, laptop (or PDA), phone-based, or wristwatch
Students are not allowed to share calculators within a testing session.
Test administrators must confirm that memory on all calculators has been cleared before and after the testing sessions.
If schools or districts permit students to bring their own hand-held calculators, test administrators must confirm that the calculators meet all the
requirements as defined above.
Resources
• Guide to the EOC Equation Builder Algebra I and Geometry: provides teachers with information on using the equation builder within the open-response
boxes
• EAGLE: provides teachers a bank of questions that can be used for instructional and assessment purposes
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•
•
•
•
•
•
•
•
•
2016-2017 Sample Test Items Geometry: includes sample items for all parts of the assessment, annotations explaining each item, and authentic student
responses representing different score points for the constructed-response section 3
Online Tools Training: provides teachers and students the opportunity to become familiar with the online testing platform and its available tools
Overview of 2016-2017 Summative Assessments: provides an overview of the 2016-2017 statewide summative assessments
K-12 Louisiana Student Standards for Math: explains the development of and lists the math content standards that Louisiana students need to master
Geometry - Teachers Companion Document PDF or word doc: contains descriptions of each standard to answer questions about the standard’s meaning
and how it applies to student knowledge and performance
Geometry Remediation Guide: reference guide for teachers to help them more quickly identify the specific remedial standards necessary for every
standard, includes information on content emphasis
Geometry Crosswalk: shows specifically how the math standards have changed from 2015-2016 to 2016-2017
K-12 LSSM Alignment to Rigor: provides explanations and a standards-based alignment to assist teachers in providing the first of those: a rigorous
education
9-12 Grade Math Teachers Toolbox: provides links to resources, such as the standards, shared teacher resources, remediation guides, and instructional
plans
Geometry Student Standards 4
Reporting Category 1: Geometry – Congruence
GM: G-CO.A
Experiment with transformations in the plane.
GM: G-CO.A.1
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a
line, and distance around a circular arc.
GM: G-CO.A.2
Represent transformations in the plane using, e.g., transparencies, tracing paper, or geometry software; describe transformations as functions that take
points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g.,
translation versus horizontal stretch).
GM: G-CO.A.3
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
GM: G-CO.A.4
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
GM: G-CO.A.5
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry
software. Specify a sequence of transformations that will carry a given figure onto another.
GM: G-CO.B
Understand congruence in terms of rigid motions.
GM: G-CO.B.6
Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the
definition of congruence in terms of rigid motions to decide if they are congruent.
GM: G-CO.B.7
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and
corresponding pairs of angles are congruent.
3
The items assembled in this document have been previously available in separate documents released in 2013-2014 and 2014-2015. Additionally, these items have been
reviewed by the LDOE to confirm alignment to the newly adopted LSSM.
4
Test items aligned to statistics standards may appear as embedded field-test items, but are not listed in student standards tables because student performance on such items
will not impact student test scores.
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GM: G-CO.B.8
GM: G-CO.C
GM: G-CO.C.9
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
Prove and apply geometric theorems.
Prove and apply theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate
interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant
from the segment's endpoints.
GM: G-CO.C.10 Prove and apply theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are
congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
GM: G-CO.C.11 Prove and apply theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a
parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
GM: G-CO.D
Make geometric constructions.
GM: G-CO.D.12 Make formal geometric constructions with a variety of tools and methods, e.g., compass and straightedge, string, reflective devices, paper folding, or
dynamic geometric software. Examples: Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines,
including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
GM: G-CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Reporting Category 2: Geometry – Similarity, Right Triangles, and Trigonometry
GM: G-SRT.A
Understand similarity in terms of similarity transformations.
GM: G-SRT.A.1 Verify experimentally the properties of dilations given by a center and a scale factor:
a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
GM: G-SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations
the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
GM: G-SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
GM: G-SRT.B
Prove and apply theorems involving similarity.
GM: G-SRT.B.4 Prove and apply theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the
Pythagorean Theorem proved using triangle similarity; SAS similarity criteria, SSS similarity criteria, ASA similarity.
GM: G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
GM: G-SRT.C
Define trigonometric ratios and solve problems involving right triangles.
GM: G-SRT.C.6 Understand that by similarity, side ratios in right triangles, including special right triangles (30-60-90 and 45-45-90), are properties of the angles in the
triangle, leading to definitions of trigonometric ratios for acute angles.
GM: G-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.
GM: G-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Reporting Category 3: Geometry – Circles | Geometry – Expressing Geometric Properties with Equations
GM: G-C.A
Understand and apply theorems about circles.
GM: G-C.A.1
Prove that all circles are similar.
GM: G-C.A.2
Identify and describe relationships among inscribed angles, radii, and chords, including the following: the relationship that exists between central, inscribed,
and circumscribed angles; inscribed angles on a diameter are right angles; and a radius of a circle is perpendicular to the tangent where the radius intersects
the circle.
GM: G-C.A.3
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
GM: G-C.B
Find arc lengths and areas of sectors of circles.
GM: G-C.B.5
Use similarity to determine that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as
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the constant of proportionality; derive the formula for the area of a sector.
Translate between the geometric description and the equation for a conic section.
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle
given by an equation.
GM: G-GPE.B
Use coordinates to prove simple geometric theorems algebraically.
GM: G-GPE.B.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the
coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
GM: G-GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a given point).
GM: G-GPE.B.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
GM: G-GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Reporting Category 4: Geometry – Geometric Measurement and Dimension | Geometry – Modeling with Geometry
GM: G-GMD.A
Explain volume formulas and use them to solve problems.
GM: G-GMD.A.1 Give an informal argument, e.g., dissection arguments, Cavalieri’s principle, and informal limit arguments, for the formulas for the circumference of a circle,
area of a circle, volume of a cylinder, pyramid, and cone.
GM: G-GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
GM: G-GMD.B
Visualize relationships between two-dimensional and three-dimensional objects.
GM: G-GMD.B.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of twodimensional objects.
GM: G-MG.A
Apply geometric concepts in modeling situations.
GM: G-MG.A.1
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
GM: G-MG.A.2
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
GM: G-MG.A.3
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with
typographic grid systems based on ratios).
GM: G-GPE.A
GM: G-GPE.A.1
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